David Cass (January 19, 1937 – April 15, 2008) was a professor of economics at the University of Pennsylvania, mostly known for his contributions to general equilibrium theory. His most famous work was on the Ramsey–Cass–Koopmans model of economic growth.
Biography David Cass was born in 1937 in Honolulu, Hawaii. He earned an A.B. in economics from the University of Oregon in 1958 and started to study law at the Harvard Law School as he thought of becoming a lawyer according to family tradition. As he hated studying law he left the program after one year and served in the army from 1959 to 1960. He then entered the economics Ph.D. program at Stanford University. Here he met Karl Shell, although the two began to work together only after both graduated. Cass's doctoral advisor was Hirofumi Uzawa, who also introduced him to Tjalling Koopmans, who at that time was a professor at Yale University. In 1965, Cass graduated with a Ph.D. in economics and statistics with a dissertation on optimal growth, with parts of the dissertation later published in the Review of Economic Studies.
After graduation Cass began to work from 1965 to 1970 as an assistant professor at the economics department of Yale University and as a research associate at the Cowles Commission for Research in Economics in New Haven. During his time at Yale University he collaborated with Menahem Yaari and Joseph Stiglitz and worked mostly on overlapping generations models. In 1970 he left New Haven for Carnegie-Mellon University in Pittsburgh, where he was a professor of economics until 1974. During his time at Carnegie-Mellon he began to collaborate with Karl Shell, who at this time was a professor at the University of Pennsylvania. One of his doctoral students was Finn E. Kydland, who would later win the Nobel Prize in Economics. In 1974 Cass left for the University of Pennsylvania, where he was a professor of economics until his death. David Cass died in 2008 in Philadelphia after a long illness. He was divorced and the father of two children.
Cass was a Guggenheim Fellow in 1970, was an elected fellow of the Econometric Society since 1972, received an honorary doctorate from the University of Geneva in 1994, was a distinguished fellow of the American Economic Association in 1999 and was an elected fellow of the American Academy of Arts and Sciences since 2003.
Research Cass made important contributions to pure economic theory, mostly in the field of general equilibrium theory. He made major contributions to the theory of optimal growth, the theory of sunspots and the theory of incomplete markets. He is perhaps best known for his article “Optimum Growth in an Aggregative Model of Capital Accumulation”, which was a part of his dissertation. In this paper he proves a necessary and sufficient condition for efficiency in the neoclassical growth model first introduced by Frank Ramsey. A major difference to the standard Ramsey growth model was that Cass considered the case where consumption in future periods is discounted, thus implicitly assuming that consumers prefer consumption today to consumption tomorrow. This modified version of the Ramsey growth model is also known as the Ramsey-Cass-Koopmans model, named after Frank Ramsey, David Cass and Tjalling Koopmans.
He was also famous for the "Cass criterion" for overlapping generations models and in the neoclassical growth model, and his work, together with Karl Shell, on the influence of extrinsic uncertainty on economic equilibria, also known as the concept of sunspot equilibria or the theory of sunspots. Together with Joseph Stiglitz he proved conditions under which it is possible for an investor to achieve an optimal portfolio under the restriction of being able to buy only two mutual funds. They also showed that generally the demand for money can not be derived from portfolio theory. Cass was also a major contributor to the theory of incomplete markets, the turnpike theory and theory of economies with markets that repeatedly open over time.
Cass's Scientific Works Dave Cass's first major contribution to economics was the characterization of optimal growth trajectories in his thesis work under Hirofumi Uzawa's supervision at Stanford University. The celebrated Cass criterion for optimal time paths in the one good growth model quickly followed. The essence of this work is the search for price characterizations of efficiency for dynamic time paths, an effort that directly pointed the way to the subsequent full dynamic decentralization of the neoclassical optimal growth model, a fact that permits its use for modeling a wide range of business cycle and other macroeconomic phenomena. Accordingly, Cass is rightly honored, together with Tjalling Koopmans and Frank Ramsey, as one of the fathers of dynamic macroeconomic analysis.
The original papers from Cass's thesis were
• "Optimum economic growth in an aggregative model of capital accumulation," published in The Review of Economic Studies in 1965 • "Optimum economic growth in the two-sector model of capital accumulation" • "Optimum economic growth in an aggregative model of capital accumulation: A turnpike theorem," published in Econometrica in 1966
The "Optimum growth ..." paper was the culmination of a long line of research (beginning with Frank Ramsey's pioneering research in the 1920s) on modeling economic growth. The literature found expression in the post-war period in the work of Robert Solow at MIT and Hirofumi Uzawa at Stanford, not only as a theory of growth, but also as a tool for understanding the macroeconomy. Much of the development of the models in the literature was grounded in a set of post-war "stylized facts" that every economics Ph.D. student learns in their first year of graduate study. One of the weak links in the development of these early models was their specification of saving behavior as being exogenous and given by the empirical regularity of the consumption-income relationship, and the various (partial equilibrium) theories of consumption spending designed to explain this regularity.
Cass's paper was the first to endogenize the consumption-savings decision by deriving an optimal capital accumulation trajectory that maximized the discounted sum of utility payoffs over time. The tools that Cass used to derive his results were from the then-newly developed field of optimal control in mathematics pioneered by Lev Pontryagin. The main results in the paper are a demonstration that under now-standard assumptions on preferences and technology, the optimal accumulation sequence exists and is unique.
The other papers in Cass's thesis drew on the major insights of the "Optimum growth ..." paper by extending them to show the existence of an optimal growth trajectory in a two-sector model of capital accumulation, and the existence of a so-called turnpike growth path associated with the optimal capital accumulation trajectory in the one-sector model.
These papers were published (possibly even completed) while Cass was a research staff member and then an assistant professor at the Cowles Foundation at Yale University (1964–1967). Cass was promoted to untenured associate professor at Cowles and remained at Yale until 1970. He coauthored several more papers during this time with Joseph Stiglitz and Menahem Yaari, who were also at Yale during this period. These included:
• "A re-examination of the pure consumption loans model" (with M.E. Yaari). J Pol Econ 74, 353–367 (1966). • "Individual saving, aggregate capital accumulation and efficient growth" (with M.E. Yaari). Essays in the Theory of Optimal Economic Growth (K. Shell, ed.), MIT, 1967. • "The implications of alternative saving and expectations hypotheses for the choice of techniques and patterns of growth" (with J.E. Stiglitz). J Pol Econ 77, 586–627 (1969). • "The structure of investor preferences and asset returns, and separability in portfolio allocation" (with J.E. Stiglitz). J Econ Theory 2, 122–160 (1970). • "Present values playing the role of efficiency prices in the one-good growth model" (with M.E. Yaari). Rev Econ Studies 38, 331–339 (1971).
In the Spear and Wright Macroeconomic Dynamics interview with Cass, he indicates that his work with Manny Yaari at Yale constituted his introduction to Samuelson's consumption loans (now overlapping generations) model, which would come front and center as a major workhorse model in Cass's subsequent work with Karl Shell on sunspot equilibria. During this time, Cass also looked more deeply at the question of how individual saving behavior and efficient growth were related. The paper on present values as efficiency prices that Cass co-authored with Yaari is easily seen to be a precursor of his subsequent work at Carnegie Mellon on capital overaccumulation and efficiency which led to the famous Cass criterion for determining inefficiency. Finally, Cass's work with Stiglitz on modeling investor preferences and asset returns provided a foundation for his later work on financial general equilibrium.
Cass left Yale in 1970, describing himself as part of Yale's "junior through-put." He was recruited by Dick Cyert, then Dean of the Graduate School of Industrial Administration at Carnegie Mellon University. During his time at GSIA, Cass completed the work on capital overaccumulation, continued his work with Joe Stiglitz on asset pricing, and began work exploring the general applicability of the mathematical techniques he had used in his thesis (mathematical programming, duality and the Hamiltonian approach to dynamic control). The papers produced during this period included:
• "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," J Econ Theory 4, 200–203 (1972). • "Distinguishing inefficient competitive growth paths: A note on capital overaccumulation and rapidly diminishing future value of consumption in a fairly general model of capitalistic production." J Econ Theory 4, 224–240 (1972). • "Risk aversion and wealth effects on portfolios with many assets" (with J.E. Stiglitz). Rev Econ Studies 39, 331–354 (1972). • "On the Wicksellian point-input, point-output model of capital accumulation: A modern view (or neoclassicism slightly vindicated)." J Pol Econ 81, 71–97 (1973). • "Duality: A symmetric approach from the economist's vantage point." J Econ Theory 7, 272–295 (1974). • "The Hamiltonian representation of static competitive or efficient allocation." Essays in Modern Capital Theory, (M. Brown, K. Sato, and P. Zaremba, eds.), North-Holland, 1976. • "The structure and stability of competitive dynamical systems" (with K. Shell). J Econ Theory 12, 31–70 (1976).
While the last two papers were published after Cass left GSIA, he indicates in the interview that he began this work while he was still at Carnegie Mellon.
Cass's second seminal contribution—the notion of a so-called sunspot equilibrium in dynamic economies which he developed jointly with Karl Shell—is also the stuff of legend, and grew out of his long and productive collaboration with Karl at Penn. The early impetus for Cass's interest in this topic stemmed from work he did with Manny Yaari on overlapping generations models, and from his early acquaintance with Bob Lucas at Carnegie Mellon and Lucas's seminal work on rational expectations in dynamic economic models. To quote from the Spear-Wright interview,
I wasn’t so interested in macro, but what struck me, and this is related to some of my later work, was the assumption that [Lucas] made to solve for equilibrium, that the state variables were obvious ... Bob and I had some long discussions, and I would say, “Well Bob, why is this the actual state space in this model?” That question came up ... after I came to Penn. At some point Karl [Shell] and I started talking about that and we developed what we called the idea of sunspots.